Publication Cover
Dynamical Systems
An International Journal
Volume 34, 2019 - Issue 3
77
Views
1
CrossRef citations to date
0
Altmetric
Articles

On the effective reducibility of a class of Quasi-periodic nonlinear systems near the equilibrium

&
Pages 385-398 | Received 17 Jul 2017, Accepted 12 Sep 2018, Published online: 03 Nov 2018

References

  • L.H. Eliasson, Floquent solutions for the one-dimensional quasi-periodic Schrödinger equation, Comm. Math. Phys. 146 (1992), pp. 447–482. doi: 10.1007/BF02097013
  • H.-L. Her and J. You, Full measure reducibility for generic one-parameter family of quasi-periodic linear systems, J. Dynam. Differential Equations 20 (2008), pp. 831–866. doi: 10.1007/s10884-008-9113-6
  • R.A. Johnson and G.R. Sell, Smoothness of spectral subbundles and reducibility of quasi-periodic linear differential systems, J. Differential Equations 41 (1981), pp. 262–288. doi: 10.1016/0022-0396(81)90062-0
  • A. Jorba and Simó C., On the reducibility of linear differential equations with quasiperiodic coefficients, J. Differential Equations 98(1) (1992), pp. 111–124. doi: 10.1016/0022-0396(92)90107-X
  • A. Jorba and Simó C., On quasi-periodic perturbations of elliptic equilibrium points, SIAM J. Math. Anal. 27 (1996), pp. 1704–1737. doi: 10.1137/S0036141094276913
  • A. Jorba, Ramirez-ros R. and J. Villanueva, Effective reducibility of quasi-periodic linear equations close to constant coefficients, SIAM J. Math. Anal. 28 (1997), pp. 178–188. doi: 10.1137/S0036141095280967
  • J. Li and J. Xu, On the reducibility for a class of quasi-periodic Hamiltonian systems with small perturbation parameter, Abstr. Appl. Anal. 2011 (2011), Article ID 354063, 17 pp.
  • J. Li and J. Xu, On the effective reducibility of a class of quasi-periodic Hamiltonian systems, Qual. Theory Dyn. Syst. 14 (2015), pp. 281–290. doi: 10.1007/s12346-015-0157-9
  • J. Li and C. Zhu, On the reducibility of a class of finitely differentiable quasi-periodic linear systems, J. Math. Anal. Appl. 413(1) (2014), pp. 69–83. doi: 10.1016/j.jmaa.2013.10.077
  • X. Wang and J. Xu, On the reducibility of a class of nonlinear quasi-periodic system with small perturbation parameter near zero equilibrium point, Nonlinear Anal. 69(7) (2008), pp. 2318–2329. doi: 10.1016/j.na.2007.08.016
  • J. Xu, On the reducibility of a class of linear differential equations with quasiperiodic coefficients, Mathematika 46 (1999), pp. 443–451. doi: 10.1112/S0025579300007907

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.